Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature

Abstract

Let M be a. complete simply connected riemannian manifold of dimension n and sectional curvature K^O. Working with closed geodesically convex subsets 0 5^ MQ M, we use the fact (see Note that M is star-shaped from every point, thus contractible, and in particular simply connected.